Sample path properties of parabolic SPDEs with non constant coefficients

TL;DR

This paper investigates the regularity of solutions to a class of parabolic stochastic partial differential equations with non-constant coefficients driven by Gaussian noise, establishing existence, uniqueness, and path properties.

Contribution

It provides new results on the existence, uniqueness, and sample path regularity of solutions to non-constant coefficient parabolic SPDEs driven by Gaussian noise.

Findings

Proved existence and uniqueness of solutions.

Established space-time regularity of solutions.

Analyzed effects of non-constant coefficients on solution properties.

Abstract

We consider an SPDE driven by a parabolic second order partial differential operator with a nonlinear random external forcing defined by a Gaussian noise that is white in time and has a spatially homogeneous covariance. We prove existence and uniqueness of a random field solution to this SPDE. Our main result concerns the space-time sample path regularity of its solution.